Question

Se dă cubul ABCDA'B'C'D' cu M si N mijloacele segmentelor AB si BC.Daca aria ABCD este egala cu 144cm2 calculati
a)MN
b)d(D';MC)
Dau funda pls repede ​

Answer 1

a)

A(ABCD) = 144  } => 144 = AB² => AB = 12 cm

AB = BC

AB = 12 cm => AC = 12√2 cm

AM = MB  } => MN = linie mijlocie in Δ ABC => MN = AB/2 = 6√2 cm

BN = NC

b)

MC = √MB² + BC² = √144 + 36 = √180 = 6√5 cm

A(MDC) = A(ABCD) - 2A(MBC)

= 144 - 2×12×6/2

= 72 cm²

Duc DP ⊥ MC

A(DMC) = 72 = MC×DP/2 =>

DP = 2×A(DMC)/MC = 2×144/6√5 cm = 24√5/5 cm

D'P = √DD'+ DP

= √(12)² + (24√5/5)²

= √144 + 576/5

= √720/5 + 576/5

= √1296/√5

= 36/√5

= 36√5/5 cm